Kronseder, Thomas (2002):
Towards Nonlinear Model-Based Online Optimal Control of Chemical Engineering Plants: Parameterised Controls and Sensitivity Functions for Very Large-Scale Index-2 DAE Systems with State Dependent Discontinuities.
In: Fortschritt-Berichte VDI: Meß-, Steuerungs- und Regelungstechnik, 8, Darmstadt, Germany, VDI Verlag, Technische Universität Darmstadt,
[Ph.D. Thesis]

Abstract

In the first part of this treatise a new concept for nonlinear model-based predictive control is suggested starting from a concrete problem from industrial application in the field of chemical engineering. This concept extends and specifies currently existing NMPC approaches. A core ingredient of the control concept is in the repeated calculation of open-loop parameterised optimal controls by a direct single-shooting algorithm which has been integrated into the industrial simulation and optimisation environment OPTISIM (R) of the Linde AG. The models of the processes of interest are given by very large-scale systems of coupled di erential and algebraic equations of index two with state and time dependent discontinuities. In order to tackle with the problem of limited computational time in a real-time setting an algorithm for the fast calculation of corrections is proposed, aiming at preserving the feasibility of a previously computed control policy in the presence of disturbances. An essential component of the direct single-shooting method is the algorithm for integration and parametric sensitivity analysis of very large-scale semi-explicit index-2 DAEs. In the second part of this work this algorithm is extended with methods for the correct treatment of state and time dependent discontinuities incorporated in the process models of interest. The first method investigated for the computation of initial values for the state variables and for the transfer of sensitivity functions at discontinuities in DAEs is based on the special properties of the BDF integrator method. The second method utilises a rigorous, hybrid approch combining structural and numberical calculations. Here, initial values for the state variables are obtained by solution of a reduced system of consiststeny equations of the model DAE. The corresponding values of the sensitivity functions are computed by the solution of a reduced system of consistency equations for the associated sensitivity DAE. While the first method shows applicable to smaller problems only, the capabilities of the rigorous approach are demonstrated by the successful solution of demanding open-loop optimal control problems from chemical engineering.

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